A microscope consisting of two convex lenses of focal lengths 2 cm and 5 cm placed 20 cm apart. Where must the object be placed so that the final image (virtual) is at a distance of 25 cm from eye ?

Explanation

`1/f=1/v-1/u`
`1/5=1/(-25)-1/u_(e)rArru_(e)=-25/6cm`
Object for the eyepiece is to be at a distance of `25/6` cm to its left.

From the diagram `v_(o)+u_(e)=20cm`
`u_(e)=25/6cm`
`thereforev_(o)=95/6cm`
For the objective, `v=v_(o)=+95/6cm,f_(o)=+2cm`
`1/f=1/v-1/u`
`rArr1/2=6/95-1/u`
`rArr1/u=6/95-1/2`
`rArru=-2.29cm`
Object is to be placed at a distance of 2.29 cm to the left side of the objective.